First, the golden basic cards: In order to unlock a golden basic card, you must get a certain hero to a certain level. This is a list of which heros get which cards, and at what level those cards unlock:

There are a few other Golden Soulbound cards that have special conditions:

Reward:
Captain’s Parrot- Unlocked when you have all of the golden pirates. (Including Captain Greenskin)
Old Murk-Eye- Unlocked when you have all of the golden murlocs. YES! THAT IS ALL THE MURLOCS! That means you have to get to level 54 with the Warlock, level 54 with the Rogue, level 52 with the Priest, and level 54 with the Paladin. (Good luck, have fun with this one.)

Promotion:
Elite Tauren Chieftain- Awarded at BlizzCon 2013
Gelbin Mekkatorque- Awarded the first time you spend real money in the game during the beta.